Multi Condition Counting

I have three columns of data

Col-A-----Col-B------Col-C
1---------(blank)-----a
3---------A----------b
1---------A----------b
2---------B----------c
2---------(blank)-----c
4---------D----------a
3---------E----------a
1---------A----------b
3---------B----------c

I am trying to calculate two things:
first, a simple count of entries (non-blank) in Col-B corresponding to 'a' in col-C. Ex. for Col-C='c', the no of entries in Col-B is 2. Here I was trying SUMPRODUCT(--(Col-B range""),--(Col-C range="a")) with CTRL+SHIFT+ENTER. It doesn't work.

second, a more complex count without repetitions. Ex. for Col-C='b' and Col-B='A', the no of entries in Col-A is 1, because there are two 1's. If there would have been three 2's and four 3's the count would be just 2.